Question

The number of six-digit numbers that can be formed from the digits $1,2,3,4,5,6$ and $7$, so that digits do not repeat and the terminal digits are even is

• A. 144
• B. 72
• C. 288
• D. 720

Answer 1

Answer: (D)

Terminal digits are the first and last digits. Since, terminal digits are even.
$\therefore 1st$ place can be filled in $3$ ways and last place can be filled in $2$ ways and remaining places can be filled in
${}^5{P}_4=120$ ways
Hence, the number of six digit number, the terminal digits are even, is $3\times 120\times 2=720$.